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Author Lent, Arnold ♦ Lutz, Peter H. ♦ Herman, Gabor T.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Keyword Linear inequalities ♦ Relaxation techniques ♦ X-ray tomography ♦ Biomedical image processing ♦ Image reconstruction ♦ Mathematical programming
Abstract The problem of recovering an image (a function of two variables) from experimentally available integrals of its grayness over thin strips is of great importance in a large number of scientific areas. An important version of the problem in medicine is that of obtaining the exact density distribution within the human body from X-ray projections. One approach that has been taken to solve this problem consists of translating the available information into a system of linear inequalities. The size and the sparsity of the resulting system (typically, 25,000 inequalities with fewer than 1 percent of the coefficients nonzero) makes methods using successive relaxations computationally attractive, as compared to other ways of solving systems of inequalities. In this paper, it is shown that, for a consistent system of linear inequalities, any sequence of relaxation parameters lying strictly between 0 and 2 generates a sequence of vectors which converges to a solution. Under the same assumptions, for a system of linear equations, the relaxation method converges to the minimum norm solution. Previously proposed techniques are shown to be special cases of our procedure with different choices of relaxation parameters. The practical consequences for image reconstruction of the choice of the relaxation parameters are discussed.
Description Affiliation: The State Univ. of New York at Buffalo, Amherst, NY (Herman, Gabor T.; Lent, Arnold; Lutz, Peter H.)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2005-08-01
Publisher Place New York
Journal Communications of the ACM (CACM)
Volume Number 21
Issue Number 2
Page Count 7
Starting Page 152
Ending Page 158


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Source: ACM Digital Library